The Hodge Laplacian has recently stimulated the development of graph Laplacians and cellular sheaf Laplacians. The spectral theory of these Laplacians has significantly extended the scope of algebraic topology and data analysis. Inspired by the theory of persistent Laplacians and sheaf Laplacians, this work develops the theory of persistent sheaf Laplacians for cellular sheaves. Given a persistent module of sheaf cochain complexes, one can define the notion of persistent sheaf Laplacians. Since a point cloud with a nonzero label associated with each point gives rise to a persistent module of sheaf cochain complexes, the spectra of persistent sheaf Laplacians encodes both geometrical and non-geometrical information of the given point cloud. The theory of persistent sheaf Laplacians brings an elegant mean for combining different types of data, and has huge potential for future development.

No abstract

No abstract

No abstract